I would love to move these beauties, but have no idea when or how.
I have read it somewhere, but of course cannot find it now, that it is best to move them when they are dormant, which would be after the leaves have all pretty well died down naturally. The post below refers to Lycoris Radiata. It is a lot less hardy, and you most probably have the Lycoris Squamigera, which is a pink lily atop a bare stem in late summer.

Also, I have read that they need to be divided every 3 to 5 years and again,
I don't agree with that in that they will often sulk a season (year) or two before blooming after being moved or divided. It is imho just much better to give the bulbs plenty of space when you plant them, so they will not need disturbing for several years. Some of mine have been planted for maybe 10+ years, and are just now needing divided, as there are a lot more bulbs than there are blooms.

I dug some bulbs and gave them to a neighbor. She missed getting one planted, and a bloom emerged from the bulb anyway at the appropriate bloom time, just laying on a table in her carport.

If you leave all of the foliage in place to fade away naturally, and move them at the best time, you too may see blooms later this summer at their usual bloom time. Plant them with the base (bottom) of the bulb about 5" deep. Some of mine are probably not even that deep as the tops of some bulbs are at about ground level, yet do fine here in my zone.

Sue...chemocurl

Here is a link that might be useful: dig and divide lycoris radiata